%0 Journal Article %1 Bichara2016128 %A Bichara, D. %A Castillo-Chavez, C. %D 2016 %I Elsevier Inc. %J Mathematical Biosciences %K Animals; Article; Basic Communicable Disease Disease-free Diseases; Dynamical Dynamics Dynamics; Environmental Epidemics; Epidemiology; Global Globally Heterogeneous Human Humans; Lagrangian Nonlinear Number; Population Reproduction Vector-borne Vectors, Vectors; analysis; animal; asymptotically basic borne calculation; carrier; communicable computing; controlled disease disease, disease; dispersal; dynamical dynamics; epidemic; equilibrium; host; human; infection mathematical model; nonlinear nonlinearity; number; numerical parameters; physical population reproduction residence risk; risks; simulation; stability; stable; statistical structures; study; system; systems, systems; time, time; transmission, vector %P 128-138 %R http://dx.doi.org/10.1016/j.mbs.2016.09.006 %T Vector-borne diseases models with residence times – A Lagrangian perspective %U http://dx.doi.org/10.1016/j.mbs.2016.09.006 %V 281 %X A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts’ dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R0 is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R0≀1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R0>1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number R0, are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence. Â\copyright 2016 Elsevier Inc.

@article{Bichara2016128, abstract = {A multi-patch and multi-group modeling framework describing the dynamics of a class of diseases driven by the interactions between vectors and hosts structured by groups is formulated. Hosts{\^a}€™ dispersal is modeled in terms of patch-residence times with the nonlinear dynamics taking into account the effective patch-host size. The residence times basic reproduction number R0 is computed and shown to depend on the relative environmental risk of infection. The model is robust, that is, the disease free equilibrium is globally asymptotically stable (GAS) if R0{\^a}‰€1 and a unique interior endemic equilibrium is shown to exist that is GAS whenever R0>1 whenever the configuration of host-vector interactions is irreducible. The effects of patchiness and groupness, a measure of host-vector heterogeneous structure, on the basic reproduction number R0, are explored. Numerical simulations are carried out to highlight the effects of residence times on disease prevalence. {\^A}{\copyright} 2016 Elsevier Inc.}, added-at = {2017-11-10T22:48:29.000+0100}, affiliation = {Department of Mathematics, California State University, Fullerton, United States; Center for Computational and Applied Mathematics, 800 N. State College Blvd, Fullerton, CA, United States; Simon A. Levin Mathematical, Computational and Modeling Science Center, Arizona State University, Tempe, AZ, United States}, author = {Bichara, D. and Castillo-Chavez, C.}, author_keywords = {Basic reproduction number; Global stability; Human dispersal; Nonlinear dynamical systems; Vector-borne diseases}, biburl = {https://www.bibsonomy.org/bibtex/270445cbdb67194fa790f536d4983362d/ccchavez}, coden = {MABIA}, correspondence_address1 = {Bichara, D.; Department of Mathematics, California State UniversityUnited States; email: dbichara@fullerton.edu}, date-added = {2017-11-10 21:45:26 +0000}, date-modified = {2017-11-10 21:45:26 +0000}, document_type = {Article}, doi = {http://dx.doi.org/10.1016/j.mbs.2016.09.006}, interhash = {5a9c527cf0274552e360c71aa9d1fbcd}, intrahash = {70445cbdb67194fa790f536d4983362d}, issn = {00255564}, journal = {Mathematical Biosciences}, keywords = {Animals; Article; Basic Communicable Disease Disease-free Diseases; Dynamical Dynamics Dynamics; Environmental Epidemics; Epidemiology; Global Globally Heterogeneous Human Humans; Lagrangian Nonlinear Number; Population Reproduction Vector-borne Vectors, Vectors; analysis; animal; asymptotically basic borne calculation; carrier; communicable computing; controlled disease disease, disease; dispersal; dynamical dynamics; epidemic; equilibrium; host; human; infection mathematical model; nonlinear nonlinearity; number; numerical parameters; physical population reproduction residence risk; risks; simulation; stability; stable; statistical structures; study; system; systems, systems; time, time; transmission, vector}, language = {English}, pages = {128-138}, publisher = {Elsevier Inc.}, pubmed_id = {27622812}, timestamp = {2017-11-10T22:48:29.000+0100}, title = {Vector-borne diseases models with residence times {\^a}€“ A Lagrangian perspective}, url = {http://dx.doi.org/10.1016/j.mbs.2016.09.006}, volume = 281, year = 2016 }